Question

Simplify
`(3-2√(5))/(√(5)-1)` giving your answer in the form
`p+q√(5)`, where p and q are rational numbers.

Answer 1

Answer:
`(-7)/(4) + (1)/(4) √(5)`

Explanation:

You have to rationalise the denominator
`√(5) - 1` in this case so multiply the whole equation by
`(√(5) + 1)/(√(5) + 1)` (this is in fact multiplying by 1 since the top and bottom of the fraction are the same).

So then you would get
`(3√(5) - 10 + 3 - 2√(5) )/(5-1)`

then
`(-7 + √(5))/(4)`

so p =
`(-7)/(4)` and q =
`(1)/(4)`